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5 Answers
5

錆: This one's relatively common. It can be used to write the verb さびる, or the derived noun さび. Of the four, this is the only one I imagine you need to know. (Note that the lower-right element of 錆 can be written either 月 or 円.)

銹・鏥・鏽: These are a lot less common. 銹 and 鏥 both appear to be simplifications of 鏽, replacing the phonetic 肅 with 秀 and 宿 respectively. (Note that all three have シュウ as an ON reading!) All three are available to write the noun さび. The latter two can be treated as variants of 銹.

A few less common compounds customarily use 銹, such as 不銹鋼{ふしゅうこう} and 銹病{さびびょう}. Aside from that, I'd expect 錆 to be used most of the time.

There doesn't appear to be any real difference in meaning, at least according to my dictionaries. I could be mistaken, of course.

The character most commonly used for rust is 錆 (written with 月 instead of 円 in the 漢字源 dictionary) and it originally meant:
1) 金属の澄みきった色 - the pure, clear color of metal
2) 金属の澄みきった音の形容。また、その音。- adj. describing a clear metallic sound, or n., the sound itself

But a misunderstanding of the Chinese caused people to think this character meant rust.
日本では誤解して、金属のさびの意に用いる。

There is also the character 鉎. It is the character that originally meant rust and is said to be the character that became 錆。
The 漢字源 states: 日本では錆を金属のさびの意に使うが、鉎が本字である。

銹 means rust in Chinese and is equivalent with 錆 in terms of meaning rust as far as Japanese dictionaries go, but 銹 is not in common usage. 鏽 and 鏥 are 異字体 or variants of the same character. There is no explanation in the 広辞苑、新漢語、or 漢字源 dictionaries of any differences between 錆 and 銹, or of why these variants exist. But I think it is common knowledge among people studying Japanese that different eras produced different characters for the same meanings in both Chinese and Japanese, so this isn't out of the ordinary.

錆 is the standard for 'rust' in Japanese (it appears to have a different meaning in Chinese)、although you may see さび in kana as it is not 常用

銹 is the Chinese for 'rust', and 鏽 a variant of it. 銹 does appear to be used in some words, like 銹病{さびびょう} in Japanese but it is not common (looks to me like wikipedia often replaces it with kana rather than using 錆).

鏥 seems to be very unusual, there are a couple of placenames using it.

Generally speaking, there are often multiple kanji variants which have been used historically, of which only one is now common, in the same way as English has had multiple ways of spelling certain words, which are now mostly consistent (regional variations and changes in spelling for effect aside).